Solve for $x+\frac{1}{x}$:$$3x+\frac{2}{x}-4=2(x+9)-\left(7-\frac{1}{x}\right)$$
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3x + 2/x - 4 = 2x + 18 - 7 + 1/x
3x - 2x + 2/x - 1/x = 4 + 18 - 7
x + 1/x = 4 + 18 - 7
x + 1/x = 15
3x + 2/x - 4 = 2x + 18 - 7 + 1/x
3x - 2x + 2/x - 1/x = 4 + 18 - 7
x + 1/x = 4 + 18 - 7
x + 1/x = 15